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Characteristics of the Differential Quadrature Method and Its Improvement

机译:微分求积法的特性及其改进

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The differential quadrature method has been widely used in scientific and engineering computation. However, for the basic characteristics of time domain differential quadrature method, such as numerical stability and calculation accuracy or order, it is still lack of systematic analysis conclusions. In this paper, according to the principle of differential quadrature method, it has been derived and proved that the weighting coefficients matrix of differential quadrature method meets the importantV-transformation feature. Through the equivalence of the differential quadrature method and the implicit Runge-Kutta method, it has been proved that the differential quadrature method is A-stable ands-stages-order method. On this basis, in order to further improve the accuracy of the time domain differential quadrature method, a class of improved differential quadrature method ofs-stage 2s-order have been proposed by using undetermined coefficients method and Padé approximations. The numerical results show that the improved differential quadrature method is more precise than the traditional differential quadrature method.
机译:微分求积法已广泛用于科学和工程计算中。但是,对于时域微分正交方法的基本特性,如数值稳定性和计算精度或阶数,仍然缺乏系统的分析结论。本文根据微分求积法的原理,推导并证明了微分求积法的加权系数矩阵满足重要的V变换特性。通过微分求积法和隐式Runge-Kutta方法的等价性,证明了微分求积法是A稳定和s阶数阶方法。在此基础上,为进一步提高时域微分正交方法的精度,提出了一种采用不确定系数法和Padé逼近的改进型s级2s阶微分正交方法。数值结果表明,改进的差分正交方法比传统的差分正交方法更精确。

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